Question Type 1: Finding the tangent and normal to a polynomial at a specific value of x Exercises

Find the equations of the tangent and the normal to the curve $y = 4x^3 + x^2 - 2x + 6$ at $x = 0$. [6 marks]

Find the equations of the tangent and the normal to the curve $y = -x^4 + 2x^2 - x + 3$ at $x = 1$.

Find the equations of the tangent and the normal to the curve $y = x^3 - 6x^2 + 4x + 5$ at $x = 4$.

Find the equations of the tangent and the normal to the curve $y = x^6 - 3x^3 + 2$ at $x = 1$.

Find the equations of the tangent and the normal to the curve $y = -2x^3 + 4x + 1$ at $x = -1$.

Find the equations of the tangent and the normal to the curve $y = x^2 - 3x + 2$ at $x = 1$.

Find the equations of the tangent and the normal to the curve $y = 7x^3 - x^2 + 2$ at $x = \frac{1}{2}$.

Find the equations of the tangent and the normal to the curve $y = 5x^3 + 8x^2 + 9x + 3$ at $x = 5$.

Find the equations of the tangent and the normal to the curve $y = \frac{1}{2}x^2 + 3x - 4$ at $x = -2$.

Find the equations of the tangent and the normal to the curve $y = 3x^4 - x^2 + 7$ at the point where $x = 0$.

Find the equations of the tangent and the normal to the curve $y = 2x^5 - x^3 + 3x$ at $x = 2$.

Find the equations of the tangent and the normal to the curve $y = -x^5 + 5x^3 - x$ at $x = -2$.